home *** CD-ROM | disk | FTP | other *** search
| Unknown | 1989-05-14 | 4.8 KB |
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MacOS 8.1
|
Win98
|
DOS
view JSON data
|
view as text
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| Confidence | Program | Detection | Match Type | Support
|
|---|
| 100%
| file
| data
| default
| |
| 100%
| xdgMime
| image/x-tga
| default
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 0d 00 0a 11 f4 20 3e 45 | 69 67 5f 76 61 6c 75 65 |..... >E|ig_value|
|00000010| 73 0d 00 14 05 3a 0d 00 | 1e 32 2a 2a 2a 2a 2a 2a |s....:..|.2******|
|00000020| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000030| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000040| 2a 2a 2a 2a 2a 2a 2a 2a | 0d 00 28 30 f4 20 2a 2a |********|..(0. **|
|00000050| 2a 20 45 69 67 65 6e 76 | 61 6c 75 65 73 20 6f 66 |* Eigenv|alues of|
|00000060| 20 61 6e 20 61 72 62 69 | 74 72 61 72 79 20 6d 61 | an arbi|trary ma|
|00000070| 74 72 69 78 20 2a 2a 2a | 0d 00 32 30 f4 20 2a 2a |trix ***|..20. **|
|00000080| 2a 20 20 20 20 45 2e 44 | 2e 20 45 6e 67 65 6c 68 |* E.D|. Engelh|
|00000090| 61 72 64 74 2c 20 4d 61 | 72 63 68 20 31 39 38 39 |ardt, Ma|rch 1989|
|000000a0| 20 20 20 20 20 2a 2a 2a | 0d 00 3c 32 2a 2a 2a 2a | ***|..<2****|
|000000b0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000000c0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000000d0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 0d 00 46 05 3a 0d |********|**..F.:.|
|000000e0| 00 50 09 f2 69 6e 69 74 | 0d 00 5a 05 3a 0d 00 64 |.P..init|..Z.:..d|
|000000f0| 09 f2 6d 65 6e 75 0d 00 | 6e 05 3a 0d 00 78 0a f2 |..menu..|n.:..x..|
|00000100| 69 6e 70 75 74 0d 00 82 | 05 3a 0d 00 8c 0c 73 74 |input...|.:....st|
|00000110| 61 72 74 25 3d 91 0d 00 | 96 09 f2 6d 61 69 6e 0d |art%=...|...main.|
|00000120| 00 a0 0a 65 6e 64 25 3d | 91 0d 00 aa 05 3a 0d 00 |...end%=|.....:..|
|00000130| b4 0a f2 70 72 69 6e 74 | 0d 00 be 05 e0 0d 00 c8 |...print|........|
|00000140| 4e 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |N-------|--------|
|00000150| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000160| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000170| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000180| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 0d 00 d2 0a dd |--------|---.....|
|00000190| f2 69 6e 69 74 0d 00 dc | 10 20 20 40 25 3d 26 30 |.init...|. @%=&0|
|000001a0| 41 30 41 3a db 0d 00 e6 | 05 e1 0d 00 f0 4e 2d 2d |A0A:....|.....N--|
|000001b0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000001c0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000001d0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000001e0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000001f0| 2d 2d 2d 2d 2d 2d 2d 2d | 0d 00 fa 0a dd f2 6d 65 |--------|......me|
|00000200| 6e 75 0d 01 04 07 20 20 | 87 0d 01 0e 1c 20 20 f1 |nu.... |..... .|
|00000210| 8a 33 31 2c 31 32 29 22 | 45 49 47 45 4e 56 41 4c |.31,12)"|EIGENVAL|
|00000220| 55 45 53 22 27 0d 01 18 | 21 20 20 f1 8a 32 37 2c |UES"'...|! ..27,|
|00000230| 31 34 29 22 5b 31 5d 20 | 52 61 6e 64 6f 6d 20 6d |14)"[1] |Random m|
|00000240| 61 74 72 69 78 22 0d 01 | 22 29 20 20 f1 8a 32 37 |atrix"..|") ..27|
|00000250| 2c 31 35 29 22 5b 32 5d | 20 46 69 78 65 64 20 64 |,15)"[2]| Fixed d|
|00000260| 65 6d 6f 20 35 78 34 20 | 6d 61 74 72 69 78 22 0d |emo 5x4 |matrix".|
|00000270| 01 2c 29 20 20 f1 8a 32 | 37 2c 31 36 29 22 5b 33 |.,) ..2|7,16)"[3|
|00000280| 5d 20 46 69 78 65 64 20 | 64 65 6d 6f 20 34 78 34 |] Fixed |demo 4x4|
|00000290| 20 6d 61 74 72 69 78 22 | 0d 01 36 05 e1 0d 01 40 | matrix"|..6....@|
|000002a0| 4e 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |N-------|--------|
|000002b0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000002c0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000002d0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000002e0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 0d 01 4a 0b dd |--------|---..J..|
|000002f0| f2 69 6e 70 75 74 0d 01 | 54 0d 20 20 77 68 69 6c |.input..|T. whil|
|00000300| 65 3d b9 0d 01 5e 0e 20 | 20 c8 95 20 77 68 69 6c |e=...^. | .. whil|
|00000310| 65 0d 01 68 0e 20 20 20 | 20 c8 8e 20 be 20 ca 0d |e..h. | .. . ..|
|00000320| 01 72 17 20 20 20 20 c9 | 20 22 31 22 3a 77 68 69 |.r. .| "1":whi|
|00000330| 6c 65 3d a3 3a ee 0d 01 | 7c 44 20 20 20 20 20 20 |le=.:...||D |
|00000340| f4 20 2a 2a 2a 20 47 65 | 6e 65 72 61 74 65 20 72 |. *** Ge|nerate r|
|00000350| 61 6e 64 6f 6d 20 6d 61 | 74 72 69 78 20 4d 2c 20 |andom ma|trix M, |
|00000360| 63 6f 6c 25 20 63 6f 6c | 75 6d 6e 73 20 61 6e 64 |col% col|umns and|
|00000370| 20 72 6f 77 25 20 72 6f | 77 73 0d 01 86 30 20 20 | row% ro|ws...0 |
|00000380| 20 20 20 20 f5 3a e8 27 | 22 20 52 6f 77 73 20 20 | .:.'|" Rows |
|00000390| 20 20 20 20 20 20 20 20 | 20 20 3a 20 22 72 6f 77 | | : "row|
|000003a0| 25 3a fd 20 72 6f 77 25 | 3e 30 0d 01 90 3d 20 20 |%:. row%|>0...= |
|000003b0| 20 20 20 20 f5 3a e8 27 | 22 20 43 6f 6c 75 6d 6e | .:.'|" Column|
|000003c0| 73 20 3c 3d 20 72 6f 77 | 73 20 3a 20 22 63 6f 6c |s <= row|s : "col|
|000003d0| 25 3a fd 20 63 6f 6c 25 | 3c 3d 72 6f 77 25 20 80 |%:. col%|<=row% .|
|000003e0| 20 63 6f 6c 25 3e 30 0d | 01 9a 39 20 20 20 20 20 | col%>0.|..9 |
|000003f0| 20 db 3a f1 27 22 20 52 | 6f 77 73 20 20 20 20 20 | .:.'" R|ows |
|00000400| 20 20 3a 20 22 c3 72 6f | 77 25 27 22 20 43 6f 6c | : ".ro|w%'" Col|
|00000410| 75 6d 6e 73 20 20 20 20 | 3a 20 22 c3 63 6f 6c 25 |umns |: ".col%|
|00000420| 0d 01 a4 19 20 20 20 20 | 20 20 72 6f 77 25 2d 3d |.... | row%-=|
|00000430| 31 3a 63 6f 6c 25 2d 3d | 31 0d 01 ae 18 20 20 20 |1:col%-=|1.... |
|00000440| 20 20 20 de 20 4d 28 72 | 6f 77 25 2c 63 6f 6c 25 | . M(r|ow%,col%|
|00000450| 29 0d 01 b8 1f 20 20 20 | 20 20 20 e3 72 25 3d 30 |).... | .r%=0|
|00000460| b8 72 6f 77 25 3a e3 63 | 25 3d 30 b8 63 6f 6c 25 |.row%:.c|%=0.col%|
|00000470| 0d 01 c2 25 20 20 20 20 | 20 20 20 20 4d 28 72 25 |...% | M(r%|
|00000480| 2c 63 25 29 3d b3 28 31 | 29 2a b4 28 30 2e 35 2d |,c%)=.(1|)*.(0.5-|
|00000490| b3 28 31 29 29 0d 01 cc | 0d 20 20 20 20 20 20 ed |.(1))...|. .|
|000004a0| 3a ed 0d 01 d6 0b 20 20 | 20 20 20 20 3a 0d 01 e0 |:..... | :...|
|000004b0| 17 20 20 20 20 c9 20 22 | 32 22 3a 77 68 69 6c 65 |. . "|2":while|
|000004c0| 3d a3 3a ee 0d 01 ea 49 | 20 20 20 20 20 20 f4 20 |=.:....I| . |
|000004d0| 2a 2a 2a 20 46 69 78 65 | 64 20 64 61 74 61 20 66 |*** Fixe|d data f|
|000004e0| 6f 72 20 64 65 6d 6f 20 | 35 78 34 20 6d 61 74 72 |or demo |5x4 matr|
|000004f0| 69 78 20 68 61 76 69 6e | 67 20 6f 6e 65 20 7a 65 |ix havin|g one ze|
|00000500| 72 6f 20 65 69 67 65 6e | 76 61 6c 75 65 0d 01 f4 |ro eigen|value...|
|00000510| 31 20 20 20 20 20 20 db | 3a f1 27 22 20 52 6f 77 |1 .|:.'" Row|
|00000520| 73 20 20 20 20 20 20 20 | 3a 20 35 22 27 22 20 43 |s |: 5"'" C|
|00000530| 6f 6c 75 6d 6e 73 20 20 | 20 20 3a 20 34 22 0d 01 |olumns | : 4"..|
|00000540| fe 20 20 20 20 20 20 20 | 72 6f 77 25 3d 34 3a 63 |. |row%=4:c|
|00000550| 6f 6c 25 3d 33 3a de 20 | 4d 28 34 2c 33 29 0d 02 |ol%=3:. |M(4,3)..|
|00000560| 08 2d 20 20 20 20 20 20 | 4d 28 30 2c 30 29 3d 34 |.- |M(0,0)=4|
|00000570| 3a 4d 28 30 2c 31 29 3d | 33 3a 4d 28 30 2c 32 29 |:M(0,1)=|3:M(0,2)|
|00000580| 3d 32 3a 4d 28 30 2c 33 | 29 3d 31 0d 02 12 2d 20 |=2:M(0,3|)=1...- |
|00000590| 20 20 20 20 20 4d 28 31 | 2c 30 29 3d 32 3a 4d 28 | M(1|,0)=2:M(|
|000005a0| 31 2c 31 29 3d 34 3a 4d | 28 31 2c 32 29 3d 31 3a |1,1)=4:M|(1,2)=1:|
|000005b0| 4d 28 31 2c 33 29 3d 33 | 0d 02 1c 2d 20 20 20 20 |M(1,3)=3|...- |
|000005c0| 20 20 4d 28 32 2c 30 29 | 3d 36 3a 4d 28 32 2c 31 | M(2,0)|=6:M(2,1|
|000005d0| 29 3d 37 3a 4d 28 32 2c | 32 29 3d 33 3a 4d 28 32 |)=7:M(2,|2)=3:M(2|
|000005e0| 2c 33 29 3d 34 0d 02 26 | 2e 20 20 20 20 20 20 4d |,3)=4..&|. M|
|000005f0| 28 33 2c 30 29 3d 38 3a | 4d 28 33 2c 31 29 3d 31 |(3,0)=8:|M(3,1)=1|
|00000600| 31 3a 4d 28 33 2c 32 29 | 3d 34 3a 4d 28 33 2c 33 |1:M(3,2)|=4:M(3,3|
|00000610| 29 3d 37 0d 02 30 2d 20 | 20 20 20 20 20 4d 28 34 |)=7..0- | M(4|
|00000620| 2c 30 29 3d 38 3a 4d 28 | 34 2c 31 29 3d 36 3a 4d |,0)=8:M(|4,1)=6:M|
|00000630| 28 34 2c 32 29 3d 34 3a | 4d 28 34 2c 33 29 3d 37 |(4,2)=4:|M(4,3)=7|
|00000640| 0d 02 3a 0b 20 20 20 20 | 20 20 3a 0d 02 44 17 20 |..:. | :..D. |
|00000650| 20 20 20 c9 20 22 33 22 | 3a 77 68 69 6c 65 3d a3 | . "3"|:while=.|
|00000660| 3a ee 0d 02 4e 46 20 20 | 20 20 20 20 f4 20 2a 2a |:...NF | . **|
|00000670| 2a 20 46 69 78 65 64 20 | 64 61 74 61 20 66 6f 72 |* Fixed |data for|
|00000680| 20 64 65 6d 6f 20 34 78 | 34 20 6d 61 74 72 69 78 | demo 4x|4 matrix|
|00000690| 20 68 61 76 69 6e 67 20 | 66 6f 75 72 20 65 69 67 | having |four eig|
|000006a0| 65 6e 76 61 6c 75 65 73 | 0d 02 58 31 20 20 20 20 |envalues|..X1 |
|000006b0| 20 20 db 3a f1 27 22 20 | 52 6f 77 73 20 20 20 20 | .:.'" |Rows |
|000006c0| 20 20 20 3a 20 34 22 27 | 22 20 43 6f 6c 75 6d 6e | : 4"'|" Column|
|000006d0| 73 20 20 20 20 3a 20 34 | 22 0d 02 62 20 20 20 20 |s : 4|"..b |
|000006e0| 20 20 20 72 6f 77 25 3d | 33 3a 63 6f 6c 25 3d 33 | row%=|3:col%=3|
|000006f0| 3a de 20 4d 28 33 2c 33 | 29 0d 02 6c 39 20 20 20 |:. M(3,3|)..l9 |
|00000700| 20 20 20 4d 28 30 2c 30 | 29 3d 31 2e 30 30 3a 4d | M(0,0|)=1.00:M|
|00000710| 28 30 2c 31 29 3d 30 2e | 34 32 3a 4d 28 30 2c 32 |(0,1)=0.|42:M(0,2|
|00000720| 29 3d 30 2e 35 34 3a 4d | 28 30 2c 33 29 3d 30 2e |)=0.54:M|(0,3)=0.|
|00000730| 36 36 0d 02 76 39 20 20 | 20 20 20 20 4d 28 31 2c |66..v9 | M(1,|
|00000740| 30 29 3d 30 2e 34 32 3a | 4d 28 31 2c 31 29 3d 31 |0)=0.42:|M(1,1)=1|
|00000750| 2e 30 30 3a 4d 28 31 2c | 32 29 3d 30 2e 33 32 3a |.00:M(1,|2)=0.32:|
|00000760| 4d 28 31 2c 33 29 3d 30 | 2e 34 34 0d 02 80 39 20 |M(1,3)=0|.44...9 |
|00000770| 20 20 20 20 20 4d 28 32 | 2c 30 29 3d 30 2e 35 34 | M(2|,0)=0.54|
|00000780| 3a 4d 28 32 2c 31 29 3d | 30 2e 33 32 3a 4d 28 32 |:M(2,1)=|0.32:M(2|
|00000790| 2c 32 29 3d 31 2e 30 30 | 3a 4d 28 32 2c 33 29 3d |,2)=1.00|:M(2,3)=|
|000007a0| 30 2e 32 32 0d 02 8a 39 | 20 20 20 20 20 20 4d 28 |0.22...9| M(|
|000007b0| 33 2c 30 29 3d 30 2e 36 | 36 3a 4d 28 33 2c 31 29 |3,0)=0.6|6:M(3,1)|
|000007c0| 3d 30 2e 34 34 3a 4d 28 | 33 2c 32 29 3d 30 2e 32 |=0.44:M(|3,2)=0.2|
|000007d0| 32 3a 4d 28 33 2c 33 29 | 3d 31 2e 30 30 0d 02 94 |2:M(3,3)|=1.00...|
|000007e0| 09 20 20 20 20 cb 0d 02 | 9e 07 20 20 ce 0d 02 a8 |. ...|.. ....|
|000007f0| 05 e1 0d 02 b2 4e 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |.....N--|--------|
|00000800| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000810| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000820| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000830| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000840| 0d 02 bc 0a dd f2 6d 61 | 69 6e 0d 02 c6 2c 20 20 |......ma|in..., |
|00000850| de 20 4d 74 28 63 6f 6c | 25 2c 72 6f 77 25 29 2c |. Mt(col|%,row%),|
|00000860| 4d 74 4d 28 63 6f 6c 25 | 2c 63 6f 6c 25 29 2c 45 |MtM(col%|,col%),E|
|00000870| 28 63 6f 6c 25 29 0d 02 | d0 1a 20 20 f2 74 72 61 |(col%)..|.. .tra|
|00000880| 6e 73 70 6f 73 65 28 4d | 28 29 2c 4d 74 28 29 29 |nspose(M|(),Mt())|
|00000890| 0d 02 da 21 20 20 f2 73 | 71 75 61 72 65 5f 73 79 |...! .s|quare_sy|
|000008a0| 6d 28 4d 28 29 2c 4d 74 | 28 29 2c 4d 74 4d 28 29 |m(M(),Mt|(),MtM()|
|000008b0| 29 0d 02 e4 1d 20 20 f2 | 65 69 67 65 6e 76 61 6c |).... .|eigenval|
|000008c0| 75 65 73 28 4d 74 4d 28 | 29 2c 45 28 29 29 0d 02 |ues(MtM(|),E())..|
|000008d0| ee 05 e1 0d 02 f8 4e 2d | 2d 2d 2d 2d 2d 2d 2d 2d |......N-|--------|
|000008e0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000008f0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000900| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000910| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000920| 2d 0d 03 02 19 dd f2 74 | 72 61 6e 73 70 6f 73 65 |-......t|ranspose|
|00000930| 28 52 28 29 2c 52 74 28 | 29 29 0d 03 0c 0d 20 20 |(R(),Rt(|)).... |
|00000940| ea 20 76 25 2c 68 25 0d | 03 16 1d 20 20 76 25 3d |. v%,h%.|... v%=|
|00000950| de 28 52 28 29 2c 31 29 | 3a 68 25 3d de 28 52 28 |.(R(),1)|:h%=.(R(|
|00000960| 29 2c 32 29 0d 03 20 34 | 20 20 e3 20 72 25 3d 30 |),2).. 4| . r%=0|
|00000970| 20 b8 20 76 25 3a e3 20 | 63 25 3d 30 20 b8 20 68 | . v%:. |c%=0 . h|
|00000980| 25 3a 52 74 28 63 25 2c | 72 25 29 3d 52 28 72 25 |%:Rt(c%,|r%)=R(r%|
|00000990| 2c 63 25 29 3a ed 3a ed | 0d 03 2a 05 e1 0d 03 34 |,c%):.:.|..*....4|
|000009a0| 4e 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |N-------|--------|
|000009b0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000009c0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000009d0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000009e0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 0d 03 3e 20 dd |--------|---..> .|
|000009f0| f2 73 71 75 61 72 65 5f | 73 79 6d 28 52 28 29 2c |.square_|sym(R(),|
|00000a00| 52 74 28 29 2c 52 74 52 | 28 29 29 0d 03 48 14 20 |Rt(),RtR|())..H. |
|00000a10| 20 52 74 52 28 29 3d 52 | 74 28 29 2e 52 28 29 0d | RtR()=R|t().R().|
|00000a20| 03 52 05 e1 0d 03 5c 4e | 2d 2d 2d 2d 2d 2d 2d 2d |.R....\N|--------|
|00000a30| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000a40| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000a50| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000a60| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000a70| 2d 2d 0d 03 66 1d dd f2 | 65 69 67 65 6e 76 61 6c |--..f...|eigenval|
|00000a80| 75 65 73 28 52 74 52 28 | 29 2c 45 56 28 29 29 0d |ues(RtR(|),EV()).|
|00000a90| 03 70 92 20 20 f4 20 2a | 2a 2a 20 20 45 69 67 65 |.p. . *|** Eige|
|00000aa0| 6e 76 61 6c 75 65 73 20 | 61 72 65 20 64 65 74 65 |nvalues |are dete|
|00000ab0| 72 6d 69 6e 65 64 20 66 | 72 6f 6d 20 52 2d 74 72 |rmined f|rom R-tr|
|00000ac0| 61 6e 73 70 6f 73 65 64 | 20 78 20 52 2c 20 75 73 |ansposed| x R, us|
|00000ad0| 69 6e 67 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |ing | |
|00000ae0| 20 20 20 20 20 20 74 68 | 65 20 70 72 6f 70 65 72 | th|e proper|
|00000af0| 74 79 20 74 68 61 74 20 | 65 69 67 65 6e 76 61 6c |ty that |eigenval|
|00000b00| 75 65 73 20 64 6f 20 6e | 6f 74 20 63 68 61 6e 67 |ues do n|ot chang|
|00000b10| 65 20 62 79 20 61 20 73 | 69 6d 69 6c 61 72 69 74 |e by a s|imilarit|
|00000b20| 79 0d 03 7a 93 20 20 f4 | 20 2a 2a 2a 20 20 74 72 |y..z. .| *** tr|
|00000b30| 61 6e 73 66 6f 72 6d 61 | 74 69 6f 6e 2e 20 52 74 |ansforma|tion. Rt|
|00000b40| 2e 52 20 69 73 20 64 65 | 63 6f 6d 70 6f 73 65 64 |.R is de|composed|
|00000b50| 20 69 6e 20 61 20 6c 6f | 77 65 72 20 61 6e 64 20 | in a lo|wer and |
|00000b60| 75 70 70 65 72 20 74 72 | 69 2d 20 20 20 20 20 20 |upper tr|i- |
|00000b70| 20 20 20 20 20 20 20 20 | 61 6e 67 75 6c 61 72 20 | |angular |
|00000b80| 6d 61 74 72 69 78 2c 20 | 52 74 2e 52 3d 4c 55 2e |matrix, |Rt.R=LU.|
|00000b90| 20 54 68 65 6e 20 55 4c | 20 68 61 73 20 74 68 65 | Then UL| has the|
|00000ba0| 20 73 61 6d 65 20 65 69 | 67 65 6e 76 61 6c 75 65 | same ei|genvalue|
|00000bb0| 73 20 61 73 0d 03 84 8a | 20 20 f4 20 2a 2a 2a 20 |s as....| . *** |
|00000bc0| 20 4c 55 2e 20 52 65 70 | 65 61 74 69 6e 67 20 74 | LU. Rep|eating t|
|00000bd0| 68 69 73 20 70 72 6f 63 | 65 73 20 69 74 65 72 61 |his proc|es itera|
|00000be0| 74 65 73 20 61 6c 6c 20 | 6e 6f 6e 2d 64 69 61 67 |tes all |non-diag|
|00000bf0| 6f 6e 61 6c 20 65 6c 65 | 6d 65 6e 74 73 20 20 20 |onal ele|ments |
|00000c00| 20 20 20 20 20 20 20 20 | 20 20 20 74 6f 20 30 2c | | to 0,|
|00000c10| 20 61 6e 64 20 74 68 65 | 20 64 69 61 67 6f 6e 61 | and the| diagona|
|00000c20| 6c 20 65 6c 65 6d 65 6e | 74 73 20 74 6f 20 74 68 |l elemen|ts to th|
|00000c30| 65 20 65 69 67 65 6e 76 | 61 6c 75 65 73 2e 0d 03 |e eigenv|alues...|
|00000c40| 8e 07 20 20 3a 0d 03 98 | 37 20 20 f4 20 2a 2a 2a |.. :...|7 . ***|
|00000c50| 2a 2a 2a 2a 2a 20 20 45 | 2e 44 2e 20 45 6e 67 65 |***** E|.D. Enge|
|00000c60| 6c 68 61 72 64 74 2c 20 | 4d 61 72 63 68 20 31 39 |lhardt, |March 19|
|00000c70| 38 39 20 20 2a 2a 2a 2a | 2a 2a 2a 2a 0d 03 a2 07 |89 ****|****....|
|00000c80| 20 20 3a 0d 03 ac 37 20 | 20 ea 20 4c 28 29 2c 55 | :...7 | . L(),U|
|00000c90| 28 29 2c 55 4c 28 29 2c | 68 25 2c 63 25 2c 72 25 |(),UL(),|h%,c%,r%|
|00000ca0| 2c 74 25 2c 72 65 70 65 | 61 74 2c 6d 61 78 2c 69 |,t%,repe|at,max,i|
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|00000cc0| 68 25 3d de 28 45 56 28 | 29 2c 31 29 0d 03 c0 23 |h%=.(EV(|),1)...#|
|00000cd0| 20 20 de 20 4c 28 68 25 | 2c 68 25 29 2c 55 28 68 | . L(h%|,h%),U(h|
|00000ce0| 25 2c 68 25 29 2c 55 4c | 28 68 25 2c 68 25 29 0d |%,h%),UL|(h%,h%).|
|00000cf0| 03 ca 07 20 20 3a 0d 03 | d4 42 20 20 f1 8a 31 2c |... :..|.B ..1,|
|00000d00| 33 30 29 22 49 74 65 72 | 61 74 69 6f 6e 20 20 20 |30)"Iter|ation |
|00000d10| 20 20 20 20 3a 20 22 20 | 3a f4 20 2a 2a 2a 20 54 | : " |:. *** T|
|00000d20| 68 69 73 20 69 6e 66 6f | 20 6d 61 79 20 62 65 20 |his info| may be |
|00000d30| 6c 65 66 74 20 6f 75 74 | 0d 03 de 07 20 20 3a 0d |left out|.... :.|
|00000d40| 03 e8 0e 20 20 72 65 70 | 65 61 74 3d b9 0d 03 f2 |... rep|eat=....|
|00000d50| 07 20 20 f5 0d 03 fc 42 | 20 20 20 20 69 74 65 72 |. ....B| iter|
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|00000d70| 33 30 29 69 74 65 72 61 | 74 69 6f 6e 73 25 20 20 |30)itera|tions% |
|00000d80| 3a f4 20 2a 2a 2a 20 6d | 61 79 20 62 65 20 6c 65 |:. *** m|ay be le|
|00000d90| 66 74 20 6f 75 74 0d 04 | 06 2f 20 20 20 20 f4 20 |ft out..|./ . |
|00000da0| 2a 2a 2a 20 43 61 6c 63 | 75 6c 61 74 65 20 6c 6f |*** Calc|ulate lo|
|00000db0| 77 65 72 20 74 72 69 61 | 6e 67 6c 65 20 4c 20 6f |wer tria|ngle L o|
|00000dc0| 66 20 52 74 52 0d 04 10 | 20 20 20 20 20 e3 20 63 |f RtR...| . c|
|00000dd0| 25 3d 30 20 b8 20 68 25 | 3a e3 20 72 25 3d 63 25 |%=0 . h%|:. r%=c%|
|00000de0| 20 b8 20 68 25 0d 04 1a | 25 20 20 20 20 20 20 4c | . h%...|% L|
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|00000e00| 25 29 3a 74 25 3d 63 25 | 2d 31 0d 04 24 43 20 20 |%):t%=c%|-1..$C |
|00000e10| 20 20 20 20 e7 20 74 25 | 3e 3d 30 20 e3 74 25 3d | . t%|>=0 .t%=|
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|00000e30| 3d 4c 28 72 25 2c 63 25 | 29 2d 4c 28 72 25 2c 74 |=L(r%,c%|)-L(r%,t|
|00000e40| 25 29 2a 4c 28 63 25 2c | 74 25 29 3a ed 0d 04 2e |%)*L(c%,|t%):....|
|00000e50| 2e 20 20 20 20 20 20 e7 | 20 72 25 3e 63 25 20 8c |. .| r%>c% .|
|00000e60| 20 4c 28 72 25 2c 63 25 | 29 3d 4c 28 72 25 2c 63 | L(r%,c%|)=L(r%,c|
|00000e70| 25 29 2f 4c 28 63 25 2c | 63 25 29 0d 04 38 39 20 |%)/L(c%,|c%)..89 |
|00000e80| 20 20 20 20 20 e7 20 72 | 25 3d 63 25 20 e7 20 4c | . r|%=c% . L|
|00000e90| 28 72 25 2c 63 25 29 3c | 30 20 8c 3a e3 20 74 25 |(r%,c%)<|0 .:. t%|
|00000ea0| 3d 30 20 b8 20 68 25 3a | 4c 28 74 25 2c 63 25 29 |=0 . h%:|L(t%,c%)|
|00000eb0| 3d 30 3a ed 0d 04 42 25 | 20 20 20 20 20 20 e7 20 |=0:...B%| . |
|00000ec0| 72 25 3d 63 25 20 4c 28 | 72 25 2c 63 25 29 3d b6 |r%=c% L(|r%,c%)=.|
|00000ed0| 20 4c 28 72 25 2c 63 25 | 29 0d 04 4c 24 20 20 20 | L(r%,c%|)..L$ |
|00000ee0| 20 20 20 e7 20 72 25 3d | 63 25 20 80 20 4c 28 72 | . r%=|c% . L(r|
|00000ef0| 25 2c 63 25 29 3d 30 20 | 72 25 3d 68 25 0d 04 56 |%,c%)=0 |r%=h%..V|
|00000f00| 0b 20 20 20 20 ed 3a ed | 0d 04 60 09 20 20 20 20 |. .:.|..`. |
|00000f10| 3a 0d 04 6a 1b 20 20 20 | 20 f2 74 72 61 6e 73 70 |:..j. | .transp|
|00000f20| 6f 73 65 28 4c 28 29 2c | 55 28 29 29 0d 04 74 09 |ose(L(),|U())..t.|
|00000f30| 20 20 20 20 3a 0d 04 7e | 48 20 20 20 20 f4 20 2a | :..~|H . *|
|00000f40| 2a 2a 20 4d 61 74 72 69 | 78 20 73 69 6d 69 6c 61 |** Matri|x simila|
|00000f50| 72 20 74 6f 20 52 74 52 | 20 28 69 2e 65 2e 20 68 |r to RtR| (i.e. h|
|00000f60| 61 76 69 6e 67 20 73 61 | 6d 65 20 65 69 67 65 6e |aving sa|me eigen|
|00000f70| 76 61 6c 75 65 73 29 20 | 69 73 20 55 4c 0d 04 88 |values) |is UL...|
|00000f80| 14 20 20 20 20 55 4c 28 | 29 3d 55 28 29 2e 4c 28 |. UL(|)=U().L(|
|00000f90| 29 0d 04 92 09 20 20 20 | 20 3a 0d 04 9c 41 20 20 |).... | :...A |
|00000fa0| 20 20 f4 20 2a 2a 2a 20 | 44 65 74 65 72 6d 69 6e | . *** |Determin|
|00000fb0| 65 20 69 66 20 64 69 61 | 67 6f 6e 61 6c 73 20 6f |e if dia|gonals o|
|00000fc0| 66 20 52 74 52 20 61 6e | 64 20 55 4c 20 61 72 65 |f RtR an|d UL are|
|00000fd0| 20 65 71 75 69 76 61 6c | 65 6e 74 0d 04 a6 0c 20 | equival|ent.... |
|00000fe0| 20 20 20 74 25 3d 30 0d | 04 b0 09 20 20 20 20 f5 | t%=0.|... .|
|00000ff0| 0d 04 ba 2a 20 20 20 20 | 20 20 e7 20 55 4c 28 74 |...* | . UL(t|
|00001000| 25 2c 74 25 29 3c 3e 52 | 74 52 28 74 25 2c 74 25 |%,t%)<>R|tR(t%,t%|
|00001010| 29 3a 72 65 70 65 61 74 | 3d a3 0d 04 c4 20 20 20 |):repeat|=.... |
|00001020| 20 20 20 20 74 25 2b 3d | 31 3a e7 20 74 25 3e 68 | t%+=|1:. t%>h|
|00001030| 25 20 72 65 70 65 61 74 | 3d a3 0d 04 ce 12 20 20 |% repeat|=..... |
|00001040| 20 20 fd 20 72 65 70 65 | 61 74 3d a3 0d 04 d8 24 | . repe|at=....$|
|00001050| 20 20 20 20 e7 20 74 25 | 3c 3d 68 25 20 72 65 70 | . t%|<=h% rep|
|00001060| 65 61 74 3d b9 3a 52 74 | 52 28 29 3d 55 4c 28 29 |eat=.:Rt|R()=UL()|
|00001070| 0d 04 e2 10 20 20 fd 20 | 72 65 70 65 61 74 3d a3 |.... . |repeat=.|
|00001080| 0d 04 ec 07 20 20 3a 0d | 04 f6 46 20 20 f4 20 2a |.... :.|..F . *|
|00001090| 2a 2a 20 50 75 74 20 65 | 69 67 65 6e 76 61 6c 75 |** Put e|igenvalu|
|000010a0| 65 73 20 73 6d 61 6c 6c | 65 72 20 74 68 65 6e 20 |es small|er then |
|000010b0| 6e 6f 6e 2d 64 69 61 67 | 6f 6e 61 6c 20 65 6c 65 |non-diag|onal ele|
|000010c0| 6d 65 6e 74 73 20 74 6f | 20 7a 65 72 6f 0d 05 00 |ments to| zero...|
|000010d0| 1f 20 20 e3 20 74 25 3d | 30 20 b8 20 68 25 3a 55 |. . t%=|0 . h%:U|
|000010e0| 4c 28 74 25 2c 74 25 29 | 3d 30 3a ed 0d 05 0a 1f |L(t%,t%)|=0:.....|
|000010f0| 20 20 e3 20 72 25 3d 31 | 20 b8 20 68 25 2d 31 3a | . r%=1| . h%-1:|
|00001100| e3 20 63 25 3d 31 20 b8 | 20 72 25 0d 05 14 29 20 |. c%=1 .| r%...) |
|00001110| 20 20 20 e7 20 94 20 55 | 4c 28 72 25 2c 63 25 29 | . . U|L(r%,c%)|
|00001120| 3e 6d 61 78 20 6d 61 78 | 3d 94 20 55 4c 28 72 25 |>max max|=. UL(r%|
|00001130| 2c 63 25 29 0d 05 1e 09 | 20 20 ed 3a ed 0d 05 28 |,c%)....| .:...(|
|00001140| 11 20 20 e3 20 63 25 3d | 30 20 b8 20 68 25 0d 05 |. . c%=|0 . h%..|
|00001150| 32 30 20 20 20 20 45 56 | 28 63 25 29 3d 52 74 52 |20 EV|(c%)=RtR|
|00001160| 28 63 25 2c 63 25 29 3a | e7 20 45 56 28 63 25 29 |(c%,c%):|. EV(c%)|
|00001170| 3c 3d 6d 61 78 20 45 56 | 28 63 25 29 3d 30 0d 05 |<=max EV|(c%)=0..|
|00001180| 3c 07 20 20 ed 0d 05 46 | 07 20 20 3a 0d 05 50 05 |<. ...F|. :..P.|
|00001190| e1 0d 05 5a 4e 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |...ZN---|--------|
|000011a0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000011b0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000011c0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000011d0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 0d |--------|-------.|
|000011e0| 05 64 0b dd f2 70 72 69 | 6e 74 0d 05 6e 0a 20 20 |.d...pri|nt..n. |
|000011f0| ef 20 31 34 0d 05 78 35 | 20 20 db 3a f1 27 22 20 |. 14..x5| .:.'" |
|00001200| 52 6f 77 73 20 20 20 20 | 20 20 20 3a 20 22 c3 72 |Rows | : ".r|
|00001210| 6f 77 25 27 22 20 43 6f | 6c 75 6d 6e 73 20 20 20 |ow%'" Co|lumns |
|00001220| 20 3a 20 22 c3 63 6f 6c | 25 0d 05 82 2e 20 20 f1 | : ".col|%.... .|
|00001230| 27 22 20 54 69 6d 65 28 | 63 65 6e 74 69 73 65 63 |'" Time(|centisec|
|00001240| 73 29 20 3a 20 22 3b c3 | 28 65 6e 64 25 2d 73 74 |s) : ";.|(end%-st|
|00001250| 61 72 74 25 29 27 27 0d | 05 8c 22 20 20 f1 22 20 |art%)''.|.." ." |
|00001260| 2a 2a 2a 2a 2a 2a 2a 2a | 20 45 69 67 65 6e 76 61 |********| Eigenva|
|00001270| 6c 75 65 73 20 3a 20 22 | 27 0d 05 96 13 20 20 e3 |lues : "|'.... .|
|00001280| 20 63 25 3d 30 20 b8 20 | 63 6f 6c 25 0d 05 a0 0f | c%=0 . |col%....|
|00001290| 20 20 20 20 f1 20 45 28 | 63 25 29 0d 05 aa 09 20 | . E(|c%).... |
|000012a0| 20 ed 3a f1 0d 05 b4 0a | 20 20 ef 20 31 35 0d 05 | .:.....| . 15..|
|000012b0| be 05 e1 0d 05 c8 4e 2d | 2d 2d 2d 2d 2d 2d 2d 2d |......N-|--------|
|000012c0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000012d0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000012e0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000012f0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001300| 2d 0d ff | |-.. | |
+--------+-------------------------+-------------------------+--------+--------+
